Hydraulic Machine

ABSTRACT

A hydraulic machine is disclosed, with a gearwheel, which has a midpoint (6) and a predetermined number of external teeth, and an annular gear, which has a midpoint (7) offset by an eccentricity (E) with respect to the midpoint (6) of the gearwheel and a number of internal teeth which exceeds by one the number of external teeth, the gearwheel and annular gear orbiting and/or rotating relative to one another and at least the form of the external teeth being created using a set of circles (30, 30&#39;; 35, 35&#39;) lying with their midpoints (P1-P6; P1&#39;-P6&#39;) on a trochoid (36, 37). It is desirable for the efficiency, service life and noise properties of such a machine to be improved. To that end, at least two trochoids (36, 37), displaced relative to one another in the circumferential direction, are provided for generating a tooth profile, the rolling circles (28, 33) of which and the base circles (27, 32) of which differ from one another.

The invention relates to a hydraulic machine with a gearwheel, which hasa midpoint and a predetermined number of external teeth with tooth tipsand tooth flanks separated by tooth spaces, and an annular gear, whichhas a midpoint offset by an eccentricity with respect to the midpoint ofthe gearwheel and a number of internal teeth with tooth tips and toothflanks separated by tooth spaces which exceeds by one the number ofexternal teeth, the gearwheel and annular gear orbiting and/or rotatingrelative to one another and at least the form of the external teethbeing created using a set of circles lying with their midpoints on atrochoid.

Such a machine is known, for example from U.S. Pat. No. 2,421,463. The(n+1) internal teeth of the annular gear consist either of freecylindrical rollers or of fixed cylinder segments. The n external teethof the gearwheel are produced by a set of circles, the circles of whichlie with their midpoints on a cycloid. The cycloid is created in that arolling circle rolls on a base circle without slipping, the base circlehaving a diameter n-times that of the rolling circle. The cycloid isgenerated from a point in the rolling circle which is spaced a distancefrom the centre of the rolling circle corresponding to the eccentricity.

The same cycloid can also be created (FIG. 2) in that a different pairof circles (RH, RK) roll on one another; here the rolling circle (RK)encloses the base circle (RH) (Dubbel, 13th edition, 1970, page 144,FIG. 138).

In the known machine, all the teeth of the gearwheel mesh simultaneouslywith the corresponding teeth of the annular gear. As many chamberssealed with respect to one another are formed as there are internalteeth in the annular gear. In theory only two pressure regions separatedfrom one another are necessary, however, of which one is pressurizedwith the pressure on the discharge side and the other is pressurizedwith the pressure on the inlet side. The larger number of contact pointscan lead to overdefinition of the system and thus to an increase inleakages. The known construction is also unfavourable because in oneposition, in which two tooth tips of an internal tooth and an externaltooth lie opposite one another, a good seal is required between thepressures on the discharge and inlet sides, but in the opposing regionforces between the gearwheel and the annular gear have to beaccommodated. In this position, the gearwheel is, as it were, clamped inthe annular gear. The tip of the external tooth touches the bottom landof the tooth space, which leads to tangential contact between tooth tipand bottom land (see FIG. 1a). This contact is poorly suited to transferof forces. The transfer of force between gearwheel and annular gear onthe opposite side is effected by line contact between two convexsurfaces of relatively small radius of curvature, which leads to highHertzian stresses. This can lead to damage to the lubricating film andconsequently to increased friction, which, if it does not result inlasting damage, significantly reduces the efficiency of the machine.

The invention is therefore based on the problem of improving theefficiency, service life and noise properties of a machine of the kindmentioned in the introduction.

This problem is solved in a hydraulic machine of the kind mentioned inthe introduction in that there are provided at least two trochoids,displaced relative to one another in the circumferential direction, forgenerating a tooth profile, the rolling circles of which and the basecircles of which differ from one another.

The tooth form of the external teeth of the gearwheel is now no longerdetermined exclusively by a single trochoid on which the set of curvesis arranged. On the contrary, at least two trochoids are provided. Theform of the teeth can thereby be changed, in order, for example, toavoid unnecessary contact between external teeth and internal teeth,without having to forfeit the advantageous effect of tooth generation bymeans of trochoids. It is not only the base circles of the trochoids, ofwhich there are at least two, that differ, but also the rolling circles,so that it is possible here to ensure that the required periodicity ismaintained, regardless of which of the different trochoids is being usedto generate the tooth form.

In a preferred embodiment, a first trochoid is essentially only thebasis of the set of circles for forming the tooth tips of the externalteeth. The tooth tips of the external teeth co-operate with the toothtips of the internal teeth to form a first sealing region which isresponsible for the seal between the discharge side and the inlet side.The trochoid-based set of circles can now be selected exclusively with aview to optimizing this sealing region, that is, for example, to keepthe Hertzian stresses in this region as small as possible and tooptimize the formation of the lubricating film.

It is also an advantage for the tooth tips of external teeth andinternal teeth to have substantially the same curvature. With the largeradius of curvature now possible, this allows a relatively large sealingarea which, together with the hydraulic fluid, enables a relativelylarge-area sealing zone to be formed. The hydraulic resistance in a gappossibly present between the tooth tips becomes relatively large, whichreduces leakage. The volumetric efficiency can consequently beincreased. No heed need be paid to how the tooth flanks would behavewith the same trochoid. Other curves can be used for the tooth flanksand the tooth spaces. The first trochoid is used until the gearwheel hasrotated sufficiently far in relation to the annular gear that the toothtip no longer needs to fulfil its sealing function.

It is also preferred for adjacent trochoids to change discontinuouslyinto one another at a transition point. This has a beneficial effect onthe side lying opposite the sealing point formed by the opposing toothtips. Large forces have to be transferred here, and a seal is effectedautomatically. The transition point provides improved possibilities inarranging the flank engagement of the teeth of the gearwheel and annulargear. Through this, for example, undesirable or unsuitable sections onthe tooth or tooth flank or the tooth space can be skipped over, withoutthe force transfer or the seal being adversely affected thereby.

It is especially preferred for the difference at the transition pointbetween the distance of the first trochoid from the contact point of tworolling circles of gearwheel and annular gear and the radius of theassociated set of circles to be substantially the same as the differencebetween the distance of the adjacent trochoid from the contact point andthe radius of the associated set of circles. During the change over fromone trochoid to another as a basis for the sets of circles, there arethen neither jumps nor discontinuities nor sharp edges in the toothform. On the contrary, at the transition point in the tooth form thereis an imperceptible change from one trochoid to the other, since thetangents of the respective circles of the sets of circles are identicalat this point.

Advantageously, at least in one position, in which an external tooth andan internal tooth form a sealing point in the region of their toothtips, the opposing sealing point is displaced from a diametral linetowards a tooth flank region. This precludes a tooth tip having to comeinto contact at this sealing point with a tooth space bottom land, whichhas the disadvantages mentioned in the introduction. The forces can beabsorbed considerably better in the flank region, since here twosurfaces lie one against the other.

It is here especially preferable for a contact to be formed between twosurfaces in the flank region, one of which is convexly curved and theother of which is concavely curved. The two surfaces therefore lie,shell-like, one inside the other. Despite a high force that has to beabsorbed by the surfaces, the force per unit area can be kept relativelylow since the force is distributed over a relatively large area.

Advantageously, circumferential sections are provided, in which thetooth form is formed by base forms other than trochoid-based sets ofcircles. The trochoids, of which there are at least two, do nottherefore cover the entire circumference of the gearwheel or the annulargear. The tooth forms can also have different curvatures where this isan advantage.

In that case it is especially preferable for the other curve forms to beformed by segments of a circular curve. Segments of a circular curve canbe produced very easily by rotating tools. In particular in thoseregions in which there is no contact anyway between gear wheel andannular gear, the tooth form merely requires to be constructed so thatfree movement of the annular gear and gearwheel relative to one anotheris possible. Contact at the necessary points enables an optimum seal tobe achieved with this construction.

Advantageously, the two parts gear wheel and annular gear aresupplemented in that the circumferential sections of the one part, whichare formed by the other curve forms, are associated with circumferentialsections of the other part, the form of which is constituted by a set ofcircles lying with their midpoints on a trochoid. In this way, at everycontact between the gearwheel and the annular gear a configuration isproduced in which a trochoid-based curve form engages with a differentcurve form. This guarantees that gearwheel and annular gear are able tomove relative to one another virtually without loss or with very smalllosses.

Advantageously, the tooth tips of the internal teeth are in the form ofa section of a cylinder, the radius of which is determined by the radiusof the base circle of the trochoid for generating the tooth tips of theexternal teeth and by the eccentricity. It is therefore possible for thetooth tips to have an approximately identical curvature.

The radius of the section of a cylinder is advantageously defined by thefollowing equation: ##EQU1## in which RZ is the radius of the section ofa cylinder,

RC is the radius of a midpoint circle for a sector of teeth of theannular gear,

E is the eccentricity, and

n is the number of teeth in the gearwheel.

In a preferred embodiment, the tooth tips of the internal teeth extendover an angle of rotation that corresponds to a movement of the contactpoint of the two rolling circles over approximately half a tooth pitch.The angular range is therefore dependent on the tooth tip curvatures.

An advantageous shaping of the tooth flank occurs when the inclinationof the tooth flank of the internal tooth at the end point of the toothspace bottom land corresponds to a normal on a tangent to the rollingcircle of the annular gear which passes through the end point of thebottom land. This produces a steep inclination in the tooth flank andconsequently a favourable force transfer. If the normal is not set up ona tangent, but on a secant, this is also possible in principle, butproduces a shallower tooth flank.

Accordingly, it is preferable for the inclination of the tooth flank atthe end point of the tooth tip of the internal tooth to correspond to aradial ray through the midpoint of the rolling circle. This alsoproduces a very steep tooth flank, without undercuts or similar problemsoccurring. A flatter tooth flank can also be used here.

The transition between these two flank sections, that is to say, betweenthe end points of tooth tip and bottom land, is expediently effected inthe form of an S-curve. The S-curve merges tangentially into the abovedescribed flank sections and compensates for the different slopes.

It is also possible to provide pockets in the bottom lands of gear wheeland/or annular gear. Oil under pressure, which assists sealing of thegearwheel on the opposite side starting from the pocket, can collect inthese pockets, or a connection for the admission of hydraulic fluid canbe provided at these pockets. The term "oil under pressure" means thathydraulic fluid which has been pressurized is involved here.

The invention is described hereinafter with reference to preferredembodiments in conjunction with the drawings, in which

FIGS. 1(a-c) is a diagrammatic illustration of the machine with threedifferent gearwheel positions,

FIG. 2 is a diagrammatic illustration to describe the variables used forconstruction,

FIG. 3 illustrates two different trochoids for constructing the form ofa tooth,

FIG. 4 is a diagrammatic illustration of the flank steepness of theinternal teeth of the annular gear, and

FIG. 5 is a diagrammatic illustration to explain the construction of thetooth flanks of the internal teeth of the annular gear.

A hydraulic machine 1 has a gearwheel 2 and an annular gear 3. Thegearwheel has n external teeth 4, in this particular case six externalteeth 4. The annular gear 3 has n+1 internal teeth 5, in this particularcase, seven. The number of internal teeth 5 is therefore always one morethan the number of external teeth 4. The gearwheel has a midpoint 6. Theannular gear has a midpoint 7. Both midpoints 6, 7 are offset withrespect to one another by an eccentricity E. In operation, the gearwheel2 rotates about its midpoint, whereas it orbits around the midpoint 7 ofthe annular gear 3.

The movement of gearwheel 2 and annular gear 3 can be represented by arolling circle 8 for the gearwheel 2 and a rolling circle 9 for theannular gear 3. Here, the rolling circle 8 rolls anticlockwise in therolling circle 9, the rolling circle 8 itself rotating in a clockwisedirection.

Each external tooth 4 has a tooth tip 10 and tooth flanks 11, 12.Adjacent external teeth 4 are separated by tooth spaces 13 with a bottomland 14. The same applies to the internal teeth 5. Each internal tooth 5has a tooth tip 15 and two tooth flanks 16, 17. Adjacent internal teeth5 are separated from one another by a tooth space 18 with a tooth bottomland 19. As shown only in FIG. 1b, pockets 20, 21 for oil under pressurecan be provided in the bottom lands 14, 19; as the gearwheel 2 rotatesrelative to the annular gear 3, these pockets receive displacedhydraulic fluid, which is pressurized here, or serve to feed hydraulicfluid to the appropriate chamber. It goes without saying that thepockets for oil under pressure can be provided for all bottom lands 14,19 of the gearwheel 2 and/or annular gear 3, and not just for a singletooth space in the gearwheel 2 and a single tooth space in the annulargear 3, as illustrated in FIG. 1b.

The gearwheel 2 divides the inner space of the annular gear 3 into twoseparate pressure regions. In FIG. 1a the division is indicateddiagrammatically by a hatched bar 22. The hatched bar 22 is theconnection of a first sealing point 23 between a tooth tip 10 of anexternal tooth 4 and a tooth tip 15 of an internal tooth 5 and a secondsealing point 24 between two tooth flanks 17 and 12 respectively of aninternal tooth 5 and an external tooth 4. In FIG. 1a, the seal betweenthe two tooth tips is in the process of changing from the point 23' tothe point 23. In FIG. 1b, in which the gearwheel 2 has been rotatedfurther with respect to the annular gear 3 (compare the position of thecontact point P on the rolling circles 8, 9), the sealing point 23' hasdisappeared. In the tooth tip-to-tooth tip region there is there onlythe sealing point 23. On the side of the gearwheel 2 opposite thesealing point 23 the seal is being effected at the second sealing point24 between two tooth flanks. The second sealing point 24 is thereforedisplaced with respect to a diametral line towards the tooth flanks.There is consequently no need for contact between tooth tip 10 of theexternal tooth 4 and the bottom land 19 of the annular gear 3. As can beseen from a comparison of FIGS. 1a to 1c, the second sealing point 24travels back and forth on the tooth flank 17 of the internal toothbetween an upper limit 25 and a lower limit 26. Outside these two limitsthere is no contact between the tooth flank 17 of the internal tooth 5and the tooth flank 12 of the external tooth 4. Identical limits can befound on the opposite tooth flanks 16 and 11. The second sealing point24 is therefore formed by a face-to-face contact of two flank faces, oneof the two faces being convex and the other of the two faces beingconcave. As will be explained in conjunction with FIG. 5, the toothflank is in the form of an S-curve. The same is then also true of thetooth flank of the external tooth 4.

FIG. 1b shows a position of the gearwheel 2 in which the seal is just inthe process of changing from the sealing point 24 to the sealing point24' on the other flank of the tooth space 18. For a brief moment thereare two sealing points here. Hydraulic fluid which has been trapped inthe tooth space 18 then exerts a pressure on the gearwheel 2 to improvethe seal at the first sealing point 23. As the gearwheel 2 continues toroll in the annular gear 3, it reaches the position illustrated in FIG.1c. In so doing, the tooth tip-to-tooth tip seal of the sealing point 23changes over to the sealing point 23". The opposite tooth flank-to-toothflank seal has shifted from the sealing and force transfer point 23' tothe sealing point 24", whereas the force transfer point has shifted tothe point 24"', with the result that a desired engagement factor isachieved. The pressure in the chambers formed by the external teeth 4and the internal teeth 5 is controlled by a known slide member, notillustrated, that is to say, the individual chambers are connected inthe correct sequence to a source of pressure, for example, a pump, or toa pressure sink, for example, a tank.

The curvature of the tooth tip 15 of the internal tooth 5 corresponds tothe curvature of a portion of the envelope of a cylinder; the radius ofthe associated cylinder can be approximately determined by the followingequation for instance: ##EQU2## in which RZ is the radius of thecylinder,

RC is the radius of a midpoint circle for a sector of teeth of theannular gear 3,

n is the number of teeth in the gearwheel 2, and

E is the eccentricity.

RC is a radius which is explained in more detail in conjunction withFIG. 2. This radius RC (=RB1+RR1) corresponds to the base circle 27enlarged by the ratio of the number of teeth between the annular gear 3and the gearwheel 2, which is used to generate the trochoid used forforming the tooth tip 10 of the external teeth 4. In this way thecurvature of the two tooth tips 10, 15 of external tooth 4 and internaltooth 5 can be kept substantially the same, so that the contactstresses, in particular the Hertzian stresses, remain low. At the sametime, the sealing point 23 becomes relatively long, so that here a verygood seal-forming approximation of the two tooth tips 10, 15 isachieved. The hydraulic resistance for the hydraulic fluid becomesrelatively large, which keeps possible leakage very small. Possible wearis shared uniformly between the two components gearwheel 2 and annulargear 3.

In FIG. 2, several further variables used to construct the machine 1 areexplained in more detail. The rolling circle 8 of the gearwheel has aradius RH. The rolling circle 9 of the annular gear has a radius RK.Furthermore, a first base circle 27 which has a radius RB1 is provided.A first rolling circle 28 (RR1) rolls without slipping on this circle27, as is known from U.S. Pat. No. 2,421,463. The radius RR1 correspondsto RB1/n, where n is the number of teeth of the gearwheel. The rollingcircle 28 has a midpoint 29. The midpoint of a circle 30 of a set ofcircles not illustrated more specifically is found at the fourth pointof the parallelogram, which is otherwise determined by the points 6, 7and 29. This circle 30 has a radius RT1. The line of intersection of thecircle 30 with a straight line 31 between the contact point P betweenthe two rolling circles 8 and 9 and the midpoint of the circle 30 is apoint of the tooth tip 10 of the external tooth 4. Further points areproduced in that the rolling circle 28 rolls on the base circle 27, orthat is to say in that the rolling circle 8 rolls anticlockwise in therolling circle 9.

Also shown is an angle of tilt VK1 which is bounded by the connectionbetween the midpoint 7 of the annular gear 3 and the midpoint of thecircle 30 on the one hand, and by a straight line through the midpoint 7and the contact point P on the other hand. This angle of tilt issubsequently a measure of the distance from the diametral line of thesealing point 24 lying opposite the tooth tip-to-tooth tip sealing point23.

A trochoid change-over is shown by means of a second base circle 32which has a larger radius RB2 than the first base circle 27. A secondrolling circle 33 having a midpoint 34 and a radius RR2 rolls on thissecond base circle 32. A circle 35 of a radius RT2 is drawn around thefourth point of the parallelogram otherwise formed by the threemidpoints 6, 7 and 34. The radius RT2 is selected so that the circle 35intersects the line 31 at exactly the same point as the circle 30.

A first trochoid is generated by means of the first rolling circle 28 onthe base circle 27; by means of the set of circles formed by the circles30 the trochoid determines the form of the tooth tip 10 of the externalteeth 4. A second trochoid is determined by the second rolling circle 33which rolls without slipping on the second base circle 32; by means ofthe set of circles formed by the circles 35 the second trochoiddetermines further parts of the external teeth 4, for example, theflanks thereof. Yet more trochoids which determine other parts, forexample, the tooth spaces between the external teeth 4, can be provided.The important point here is that no point of discontinuity in the toothshould occur as a result of change-over from one trochoid to another.This is achieved in that the "boundary circles" of the respective setsof circles intersect the same point on the straight line 31.

The generation of two tooth portions by means of two different trochoidsis illustrated diagrammatically in FIG. 3. Here, a first trochoid 36with the points P1-P6 is formed by the first rolling circle 28 rollingon the first base circle 27. A second trochoid 37 is formed by thesecond rolling circle 33 which rolls on the second base circle 32. Thepoints P1'-P6' are arranged on the second trochoid 37. The points P6 ofthe first trochoid 36 and P1' of the second trochoid 37 lie on the samestraight line 31, which also passes through the contact point P betweenthe rolling circle 8 of the gearwheel and the rolling circle 9 of theannular gear. The rolling circles 28, 28' respectively for the startingand finishing point of the first trochoid 36 and the associated circles30 and 30' respectively are illustrated, and similarly the rollingcircles 33 and 33' respectively of the second trochoid 37 and theassociated circles 35, 35' respectively of the set of circles generatingthe tooth flank. In this way the first trochoid generates the tooth tip10, while the second trochoid 37 is responsible for generating the toothflank 12. It is clearly recognisable that the circle 30' and the circle35 intersect the line 31 at the same point, producing here a smoothtransition on the tooth form. The change-over from one trochoid 36 tothe other trochoid 37 does not therefore lead to any jumps ordiscontinuities in the tooth form. The second trochoid 37 can now beused for generating the tooth flanks and the tooth spaces. Only when atooth tip is approached again during continued movement in thecircumferential direction is a first trochoid 36 required again. Duringthe transition from the second trochoid 37 to the first trochoid 36 acorresponding enlargement of the angle of tilt VK2 to VK1 (FIG. 2) iseffected, thus compensating again for an angular displacement effectedby the transition to the second trochoid 37. In FIG. 3 the direction ofrotation of the rolling circle 8 in the rolling circle 9 is opposite tothe direction in FIG. 1, to show that the circumferential direction hasno bearing on generation of the tooth form.

In FIG. 2 a further circle 38 of radius RC is drawn in. The radius RCcan be regarded as base circle for the annular gear 3. The radius RCcorresponds to (n+1) times the radius RR1, that is to say, itcorresponds to the radius RB1 of the first base circle 27 enlarged bythe ratio of the number of teeth in the annular gear 3 and in thegearwheel 2. Using the radius RC of the circle 38, the curvature at thetooth tip 15 of the internal teeth 5 can now be determined. Using theradius RC and the eccentricity E, this radius RZ (FIG. 4) is given bythe following equation ##EQU3## In this way it is possible for the toothtips 10, 15 of external teeth 4 and internal teeth 5 to havesubstantially the same radius of curvature, that is to say RT1=RZ. Sincethe tooth tip 10 of the external tooth 4 has been formed with the aid ofthe first cycloid 36, strictly speaking, one cannot refer to a radiushere. But the curvature remains in a region which is comparable with theradius RZ. Because the two tooth tips 10, 15 have substantially the samecurvature, contact stresses, in particular Hertzian stresses, becomeless. This enables a uniform lubricating film to form. Wear is largelyavoided here. Any potential residual wear is distributed uniformly overthe two components annular gear 3 and gearwheel 2. At the same time,there is a relatively long sealing point in the circumferentialdirection so that leakages here can be kept very small. A relativelygood volumetric efficiency is consequently achieved.

Since the form of the external teeth 4 has been described using FIGS. 2and 3, the construction of the internal teeth 5 of the annular gear 3and the tooth flanks thereof are now described in conjunction with FIGS.4 and 5. The tooth tip 15 is a section of a cylinder with a radius ofcurvature RZ=RT1, that is to say, this radius corresponds to the radiusof the circle 30 used to generate the tooth tip 10. In this way thecurvature of the tooth tip 10 of the internal tooth 4 corresponds to thecurvature of the tooth tip 15 of the external tooth 5. Similarly, thebottom land 19 can likewise be formed by a section of a cylinder. Theradius of this section of a cylinder can be smaller than the radius ofthe circle which touches the deepest points of the tooth spaces 18 (FIG.1b), that is to say, the points that are furthest from the midpoint ofthe annular gear 3. To simplify the description, end points 39, 40 areintroduced for tooth tip 15 and bottom land 19 respectively. These endpoints 39, 40 mark the transition from the tooth tip 15 and the bottomland 19 to the tooth flank 17. The end points 39, 40 can be formed bycylindrical segments of a small radius of curvature which produce arelatively sharp edge. The formation of an acute angle should beavoided, however.

The slope of the tooth flank 17 at the transition between the bottomland 19 and the tooth flank 17 is determined by a normal 41 on a tangent42 to the rolling circle 9 of the annular gear 3, the tangent 42 passingthrough the end point 40. In principle, it is also possible for thetangent 42 to the rolling circle 9 to be replaced by a secant. However,this would cause the slope of the tooth flank 17 to be less steep atthis point. The optimum slope of the normal 41 and consequently of thetooth flank 17 can be achieved using the tangent 42.

The slope of the tooth flank 17 at the other end point 39, that is, atthe transition between the tooth tip 15 and the tooth flank 17, isdetermined by a radial ray 43, that is, by a straight line through themidpoint 7 of the rolling circle 9 and the end point 39. The transitionbetween the two end points 39 and 40 can be formed by an S-curve.

This S-curve, as shown in FIG. 5, can be formed by at least two arcsegments 44, 45 which, like the tooth flanks of the external teeth 5 inFIG. 2, can be generated by rolling circles rolling on one another.However, in this case it is sufficient, for example, for only one of thearc segments, here segment 45, to be formed by an involute (FIG. 5). Theend point 39 of the tooth tip 15 and the slope of the flank there arefixed by the radial ray 43. The arc segment 44 can be formed by asegment of an arc of a circle which touches this tooth tip tangent 43and the arc segment 45. Such an arc of a circle can be easilyconstructed. The S-curve, which determines the tooth flank 17, is thencomposed of two arc segments 44, 45, of which one 45 starts from the endpoint 40 and the second 44 starts with the opposite curvature from theend point 39. At their contact point 17, both arc segments 44, 45 havethe same tangent. Since two points 39, 17 with associated tangents arethen available for the arc of a circle 44, the arc of a circle 44 can beeasily constructed.

The contact between the gearwheel 2 and annular gear 3 is restricted tothe two sealing regions 23 and 24, that is, in the sealing region 23only the two tooth tips 10, 15 of the external teeth 4 and the internalteeth 5 touch, while in the sealing region 24 only the tooth flanks 11,12 and 16, 17 touch.

To construct the machine, the procedure can be as follows, for example.After deciding on the number of teeth for the gearwheel 2, which in thisembodiment has been selected to be even, and for the annular gear 3, thewidth of the tooth tip 15 of the internal teeth 5 in the annular gear 3is selected. The tooth tips 15 need only be the width required forsealing. The curvature of the tooth tips 15 is provided by theabove-mentioned equation for RZ. In dependence on the radius RC used inthe connection, the base circle 27 and the rolling circle 28 for thetrochoid 36 for generating the tooth tip 10 of the external teeth 4 ofthe gearwheel 2 are chosen. The construction of the tooth tip iseffected as given in U.S. Pat. No. 2,421,463. The tooth tips 10 thenhave approximately the same curvature as the tooth tips 15 of theinternal teeth. The tooth spaces 18 in the annular gear 3 are selectedto be wide enough for the tooth tips 10 of the gearwheel 2 to engagetherein. The tooth spaces 18 can, as shown in FIG. 1b, be made deeper bypockets 21 for oil under pressure, with the result that jamming can beavoided. The same applies to the tooth spaces 13 in the gearwheel 2.After the tooth tips 10, 15 have been constructed, the sealing point 23is determined. There are several possible methods of constructing thesealing point 24, at which two tooth flanks engage with one another. Ina first possibility, the tooth flank can be generated on the annulargear 3 by any curve, for example by the S-curve specified in combinationwith FIG. 5. After that, the second trochoid 37 (see FIG. 3) for thegearwheel 2 is determined. Alternatively, curves on the gearwheel canalso be selected. A corresponding trochoid is then used for generatingthe tooth flank form for the annular gear 3. Mixed forms can also beused, in which the form of the tooth flanks is generated partially bycurves, for example, circular curves, and partially by trochoid-basedcurves. Normally, cycloids are used for trochoids, that is, the rollingcircles roll on base circles.

The steepness of the tooth flanks should be dimensioned so that theslope-created drive forces which arise through rolling of the flanks ofinternal teeth and external teeth against one another, have a beneficialeffect on the area on which pressure acts indicated by the bar 22 inFIG. 1a. An improved seal at the sealing points 23 is achieved as aresult.

The machine illustrated gives improved noise ratios. Wear is reduced.With otherwise the same volume there is a greater efficiency, that is,the volumetric performance is increased. Since a higher pressure can beused in the sealing regions 23, 24 because of the improved sealingconditions, there is also a greater torque. With an identical outputcompared with known machines, liquids of reduced lubricity can be used,since the formation of a lubricating film is given greater support bythe structural features.

I claim:
 1. In a hydraulic machine with a gearwheel having a midpointand a predetermined number of external teeth with tooth tips and toothflanks separated by tooth spaces, and an annular gear having a midpointoffset by an eccentricity with respect to the midpoint of the gearwheeland having a number of internal teeth with tooth tips and tooth flanksseparated by tooth spaces which exceed by one the number of saidexternal teeth, the gearwheel and annular gear orbiting or rotatingrelative to one another and at least the external teeth being createdfrom a form using a set of circles lying with their midpoints on atrochoid, the improvement comprising at least two trochoids, displacedrelative to one another in a circumferential direction, for generating atooth profile, each trochoid being formed by a rolling circle and a basecircle, the rolling circles of the trochoids and the base circles of thetrochoids differing from one another.
 2. A machine according to claim 1,in which a first trochoid is the basis of the set of circles forming thetooth tips of the external teeth.
 3. A machine according to claim 1, inwhich the tooth tips of external teeth and internal teeth aresubstantially the same.
 4. A machine according to claim 1, in whichadjacent trochoids change discontinuously into one another at atransition point.
 5. A machine according to claim 4, in which thedifference at the transition point between the distance of the firsttrochoid from the contact point of two rolling circles of the gearwheeland the annular gear and the radius of a first associated set of circlesis substantially the same as the difference between the distance of anadjacent trochoid from the contact point and the radius of a secondassociated set of circles.
 6. A machine according to claim 1, in which,at least in one position, in which an external tooth and an internaltooth form a sealing point at their tooth tips, an opposing sealingpoint is displaced from a diametral line towards a tooth flank region.7. A machine according to claim 6, in which a contact is formed betweentwo surfaces in the flank region, one of the surfaces being convexlycurved and the other of the surfaces being concavely curved.
 8. Amachine according to claim 1, having circumferential sections in which atooth form is formed by base forms other than a trochoid-based sets ofcircles.
 9. A machine according to claim 8, in which the base forms arecreated by segments of a circular curve.
 10. A machine according toclaim 8, in which the gear wheel and annular gear are complementary inthat the circumferential sections of one of the gearwheel and theannular gear, which are formed by the base forms, are associated withcircumferential sections of the other of the gearwheel and the annulargear and having a form constituted by a set of circles lying with theirmidpoints on a trochoid.
 11. A machine according to claim 1, in whichthe tooth tips of the internal teeth are in the form of a section of acylinder having a radius determined by the radius of the base circle ofthe trochoid for generating the tooth tips of the external teeth and bythe eccentricity.
 12. A machine according to claim 11, in which theradius of the section of a cylinder is defined by the followingequation: ##EQU4## in which RZ is the radius of the section of acylinder,RC is the radius of a midpoint circle for a sector of teeth ofthe annular gear, E is the eccentricity, and n is the number of teeth inthe gearwheel.
 13. A machine according to claim 1, in which the toothtips of the internal teeth extend over an angle of rotation thatcorresponds to a movement of the contact point of the rolling circles ofthe trochoids over approximately half a tooth pitch.
 14. A machineaccording to claim 1, in which inclination of a tooth flank of theinternal tooth at an end point of a tooth space bottom land correspondsto a normal on a tangent to the rolling circle of the annular gear whichpasses through the end point of the bottom land.
 15. A machine accordingto claim 14, in which the inclination of the tooth flank at an end pointof a tooth tip of the internal tooth corresponds to a radial ray throughthe midpoint of the rolling circle.
 16. A machine according to claim 15,in which transition from the end point of the bottom land to the endpoint of the tooth tip is effected in the form of an S-curve.